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Simplifying 2x2 + -24x + -3955977 = 0 Reorder the terms: -3955977 + -24x + 2x2 = 0 Solving -3955977 + -24x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1977988.5 + -12x + x2 = 0 Move the constant term to the right: Add '1977988.5' to each side of the equation. -1977988.5 + -12x + 1977988.5 + x2 = 0 + 1977988.5 Reorder the terms: -1977988.5 + 1977988.5 + -12x + x2 = 0 + 1977988.5 Combine like terms: -1977988.5 + 1977988.5 = 0.0 0.0 + -12x + x2 = 0 + 1977988.5 -12x + x2 = 0 + 1977988.5 Combine like terms: 0 + 1977988.5 = 1977988.5 -12x + x2 = 1977988.5 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 1977988.5 + 36 Reorder the terms: 36 + -12x + x2 = 1977988.5 + 36 Combine like terms: 1977988.5 + 36 = 1978024.5 36 + -12x + x2 = 1978024.5 Factor a perfect square on the left side: (x + -6)(x + -6) = 1978024.5 Calculate the square root of the right side: 1406.422589409 Break this problem into two subproblems by setting (x + -6) equal to 1406.422589409 and -1406.422589409.Subproblem 1
x + -6 = 1406.422589409 Simplifying x + -6 = 1406.422589409 Reorder the terms: -6 + x = 1406.422589409 Solving -6 + x = 1406.422589409 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 1406.422589409 + 6 Combine like terms: -6 + 6 = 0 0 + x = 1406.422589409 + 6 x = 1406.422589409 + 6 Combine like terms: 1406.422589409 + 6 = 1412.422589409 x = 1412.422589409 Simplifying x = 1412.422589409Subproblem 2
x + -6 = -1406.422589409 Simplifying x + -6 = -1406.422589409 Reorder the terms: -6 + x = -1406.422589409 Solving -6 + x = -1406.422589409 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -1406.422589409 + 6 Combine like terms: -6 + 6 = 0 0 + x = -1406.422589409 + 6 x = -1406.422589409 + 6 Combine like terms: -1406.422589409 + 6 = -1400.422589409 x = -1400.422589409 Simplifying x = -1400.422589409Solution
The solution to the problem is based on the solutions from the subproblems. x = {1412.422589409, -1400.422589409}
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